The correct answer is 9.57%. but I want to know how to solve it

5.6 A certain electrical appliance is sold with a 5-year guarantee. This provides that the full purchase price is refunded if the product fails within 2 years, and half of the purchase price is refunded if the product fails in the following 3 years. A study shows that out of a typical batch of 100 items, there will be 2 failures in the first year, 3 failures in the second year and 4 failures per year after that. Assuming that interest is a constant 5% and that reimbursement is made at the end of the year of failure, what is the cost of this guarantee to the manufacturer, as a percentage of the purchase price